Woven tubular vascular prostheses having a fork are known from EP 0 108 171 B1 and EP 0 910 310 B1 (which corresponds to DE 697 28 268 T2). Such forks are also referred to as furcations or bifurcations or trifurcations. The problem with vascular prostheses having forks is that leakage may occur in the furcation region, or in the crotch of the fork. This leakage is due to an additional area in the crotch region at the transition point from the large diameter to the small diameters, which cannot be covered to the required density with the number of yarns given. This problem is described in detail in DE 697 28 268 T2.